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A centralized heterogeneous formation flight position control scheme has been formulated using an explicit model following design, based on a Linear Quadratic Regulator Proportional Integral (LQR PI) controller. The leader quadcopter is a stable reference model with desired dynamics whose output is perfectly tracked by the two wingmen quadcopters. The leader itself is controlled through the pole placement control method with desired stability characteristics, while the two followers are controlled through a robust and adaptive LQR PI control method. Selected 3-D formation geometry and static stability are maintained under a number of possible perturbations. With this control scheme, formation geometry may also be switched to any arbitrary shape during flight, provided a suitable collision avoidance mechanism is incorporated. In case of communication loss between the leader and any of the followers, the other follower provides the data, received from the leader, to the affected follower. The stability of the closed-loop system has been analyzed using singular values. The proposed approach for the tightly coupled formation flight of mini unmanned aerial vehicles has been validated with the help of extensive simulations using MATLAB/Simulink, which provided promising results.